One has to recall, on this question, the capacitor plague problem that the computer industry experienced for a number of years. The issue with this is I'm not sure if there was ever a way to discover these effects prior to failure, and the main mitigation method was a supply-chain change.
However, it does give perspective. As Aravinthkumar (answerer here) suggests, random component testing does weed out a fairly good number of bad components, however this will only detect components that are immediately defective. It will fail to detect components that like the capacitor plague, simply have a premature lifespan, but with no other obvious issues. Also, like you yourself said, the components are usually within specification, so no red flags are raised there.
What I suggest you do is run your own product, continuously. If it's a microprocessor-based product, develop some sort of protocol much like a benchmark that is designed to stress-test the system at maximum allowable power. Cycle the power randomly (a lot of capacitors fail on initial startup, under inrush current situations). If you're in a market segment where you don't expect your devices to be run continuously (i.e. 24h/day or close to), by doing so yourself you can detect if the components meet the specification for your product lifecycle, as well as make your determination a good deal faster than it would take the end-users to come to the same conclusion.
Pushing the components a little harder might make issues come to light quicker. As it is good engineering practice to build a margin of safety into circuits (since we're talking capacitors, presumably power supplies), push the circuit harder (i.e. current draws) within the margin of safety, not so much as to cause failure but more so than you would expect from the end user.
At any rate, once you've determined that failure in your current component supply is probable (that is, higher than the manufacturer's failure rate, or your company's own arbitrary failure rate), select a different manufacturer or device line, etc.